burgers_diffusion_operators.icc
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field lh (Float epsilon, Float t, const test& v) {
#ifdef NEUMANN
return field (v.get_vf_space(), 0);
#else // NEUMANN
size_t d = v.get_vf_space().get_geo().dimension();
size_t k = v.get_vf_space().degree();
Float beta = (k+1)*(k+d)/Float(d);
return epsilon*integrate ("boundary",
beta*penalty()*g(epsilon,t)*v
- g(epsilon,t)*dot(grad_h(v),normal()));
#endif // NEUMANN
}
field gh (Float epsilon, Float t, const field& uh, const test& v) {
return - integrate (dot(compose(f,uh),grad_h(v)))
+ integrate ("internal_sides",
compose (phi, normal(), inner(uh), outer(uh))*jump(v))
+ integrate ("boundary",
compose (phi, normal(), uh, g(epsilon,t))*v);
}
g
u_exact g
Definition: burgers_diffusion_exact.h:33
lh
field lh(Float epsilon, Float t, const test &v)
Definition: burgers_diffusion_operators.icc:25
gh
field gh(Float epsilon, Float t, const field &uh, const test &v)
Definition: burgers_diffusion_operators.icc:37
Float
see the Float page for the full documentation
field
see the field page for the full documentation
test
see the test page for the full documentation
mkgeo_ball.d
int d
Definition: mkgeo_ball.sh:154
rheolef::details::compose
class rheolef::details::field_expr_v2_nonlinear_node_unary compose
rheolef::details::dot
rheolef::details::is_vec dot
rheolef::grad_h
std::enable_if< details::is_field_convertible< Expr >::value,details::field_expr_v2_nonlinear_terminal_field< typename Expr::scalar_type,typename Expr::memory_type,details::differentiate_option::gradient >>::type grad_h(const Expr &expr)
grad_h(uh): see the expression page for the full documentation
Definition: field_expr_terminal.h:949
rheolef::integrate
std::enable_if< details::is_field_expr_v2_nonlinear_arg< Expr >::value &&! is_undeterminated< Result >::value, Result >::type integrate(const geo_basic< T, M > &omega, const Expr &expr, const integrate_option &iopt, Result dummy=Result())
see the integrate page for the full documentation
Definition: integrate.h:202
rheolef::penalty
details::field_expr_v2_nonlinear_terminal_function< details::penalty_pseudo_function< Float > > penalty()
penalty(): see the expression page for the full documentation
Definition: field_expr_terminal.h:626
rheolef::normal
details::field_expr_v2_nonlinear_terminal_function< details::normal_pseudo_function< Float > > normal()
normal: see the expression page for the full documentation
Definition: field_expr_terminal.h:439
rk::beta
Float beta[][pmax+1]
Definition: runge_kutta_semiimplicit.icc:60
f
Definition: cavity_dg.h:29
phi
Definition: phi.h:25
epsilon
Float epsilon
Definition: transmission_error.cc:25